Based on the framework of evidence theory, data fusion aims at obtaining a single Basic Probability Assignment (BPA) function by combining several belief functions from distinct information sources. Dempsters rule of combination is the most popular rule of combinations, but it is a poor solution for the management of the conflict between various information sources at the normalization step. Even when it faces high conflict information, the classical Dempster-Shafers (D-S) evidence theory can involve counter-intuitive results. This paper presents a modified averaging method to combine conflicting evidence based on the distance of evidences; and also gives the weighted average of the evidence in the system. Numerical examples showed that the proposed method can realize the modification ideas and also will provide reasonable results with good convergence efficiency.